Question

The diagram shows a circle inside a rectangle.... ​

Answer 1

Answer:

let $x$ = height of rectangle

Given:

• height of rectangle = diameter of circle
• length of rectangle = 3 × height of rectangle

Therefore,

• height of rectangle = $x$
• diameter of circle = $x$
• radius of circle = $\dfrac{1}{2}x$
• length of rectangle = $3x$

Shaded area = area of rectangle - area of circle

Area of rectangle = length × height

                             = $3x \times x$

                             = $3x^2$

Area of circle = $\pi r^2$

                       $=\pi \left(\dfrac{1}{2}x\right)^2$

                       $=\dfrac14\pi x^2$

$\implies \textsf{shaded area}=3x^2-\dfrac14\pi x^2$

If the radius = 2 cm, then the diameter ($x$) = 4 cm

Substituting $x = 4$ into the equation:

$\implies \textsf{shaded area}=3(4)^2-\dfrac14\pi (4)^2$

$\implies \textsf{shaded area}=48-4\pi$

$\implies \textsf{shaded area}=4(12-\pi) \textsf{ cm}^2$